Interstellar Dust

The first clear evidence for the existence of interstellar dust was obtained around 1930. Before that, it had been generally thought that space is completely transparent and that light can propagate indefinitely without extinction.

In 1930 Robert Trumpler published his study of the space distribution of the open clusters. The absolute magnitudes M of the brightest stars could be estimated on the basis of the spectral type. Thus the distance r to the clusters could be calculated from the observed apparent magnitudes m of the bright stars: r m - M = 5lg —— . (15.1)

10 pc

Trumpler also studied the diameters of the clusters. The linear diameter D is obtained from the apparent angular diameter d by means of the formula

where r is the distance of the cluster.

It caught Trumpler's attention that the more distant clusters appeared to be systematically larger than the nearer ones (Fig. 15.1). Since this could hardly be true, the distances of the more distant clusters must have been overestimated. Trumpler concluded that space is not completely transparent, but that the light of a star is dimmed by some intervening material. To take this into account, (15.1) has to be replaced with (4.17) r m - M = 5lg —— + A , (15.3)

10 pc where A > 0 is the extinction in magnitudes due to the intervening medium. If the opacity of the medium is assumed to be the same at all distances and in all directions, A can be written

where a is a constant. Trumpler obtained for the average value of a in the galactic plane, apg = 0.79 mag/kpc, in photographic magnitudes. At present, a value of 2 mag/kpc is used for the average extinction. Thus the extinction over a 5 kpc path is already 10 magnitudes.

Hannu Karttunen et al. (Eds.), The Interstellar Medium.

In: Hannu Karttunen et al. (Eds.), Fundamental Astronomy, 5th Edition. pp. 307-338 (2007) DOI: 11685739_15 © Springer-Verlag Berlin Heidelberg 2007

Distance [kpcj

Fig. 15.1. The diameters of open star clusters calculated with the distance given by the formula (15.1) according to Trumpler (1930). The increase of the diameter with distance is not a real phenomenon, but an effect of interstellar extinction, which was discovered in this way

Extinction due to dust varies strongly with direction. For example, visible light from the galactic centre (distance 8-9 kpc) is dimmed by 30 magnitudes. Therefore the galactic centre cannot be observed at optical wavelengths.

Extinction is due to dust grains that have diameters near the wavelength of the light. Such particles scatter light extremely efficiently. Gas can also cause extinction by scattering, but its scattering efficiency per unit mass is much smaller. The total amount of gas allowed by the Oort limit is so small that scattering by gas is negligible in interstellar space. (This is in contrast with the Earth's atmosphere, where air molecules make a significant contribution to the total extinction).

Interstellar particles can cause extinction in two ways:

1. In absorption the radiant energy is transformed into heat, which is then re-radiated at infrared wavelengths corresponding to the temperature of the dust particles.

2. In scattering the direction of light propagation is changed, leading to a reduced intensity in the original direction of propagation.

An expression for interstellar extinction will now be derived. The size, index of refraction and number density of the particles are assumed to be known. For simplicity we shall assume that all particles are spheres with the same radius a and the geometrical cross section na2. The true extinction cross section of the particles Cext will be

where Qext is the extinction efficiency factor.

Let us consider a volume element with length dl and cross section d A, normal to the direction of propagation (Fig. 15.2). It is assumed that the particles inside the element do not shadow each other. If the particle density is n, there are n dl d A particles in the volume element

Fig. 15.2. Extinction by a distribution of particles. In the volume element with length dZ and cross section dA, there are n d A dZ particles, where n is the particle density in the medium. If the extinction cross section of one particle is Cext,

the total area covered by the particles is n dA dlCext. Thus the fractional decrease in intensity over the distance dl is dI/1 = -n dA dl Cext/dA = -n Cext dl

and they will cover the fraction dr of the area d A, where n d A dl Cext dr =-—-= n Cext dl.

In the length dl the intensity is thus changed by dI = -Idr . (15.6)

On the basis of (15.6) dr can be identified as the optical depth.

The total optical depth between the star and the Earth is

= n Cext dl = Cextnr where n is the average particle density along the given path. According to (4.18) the extinction in magnitudes is

where X is the wavelength of the radiation, then

The exact expression for Qext is a series expansion in x that converges more slowly for larger values of x. When x ^ 1, the process is called Rayleigh scattering; otherwise it is known as Mie scattering. Figure 15.3 shows Qext as a function of x for m = 1.5 and m = 1.33. For very large particles, (x ^ 1) Qext = 2, as appears

Fig. 15.3. Mie scattering: the extinction efficiency factor for spherical particles for the refractive indices m = 1.5 and m = 1.33 (refractive index of water). The horizontal axis is related to the size of the particle according to x = 2na/k, where a is the particle radius and k, the wavelength of the radiation

This formula can also be inverted to calculate n, if the other quantities are known.

The extinction efficiency factor Qext can be calculated exactly for spherical particles with given radius a and refractive index m. In general,

Q abs = absorption efficiency factor, Q sca = scattering efficiency factor .

If we define

Fig. 15.3. Mie scattering: the extinction efficiency factor for spherical particles for the refractive indices m = 1.5 and m = 1.33 (refractive index of water). The horizontal axis is related to the size of the particle according to x = 2na/k, where a is the particle radius and k, the wavelength of the radiation from Fig. 15.3. Purely geometrically one would have expected Qext = 1; the two times larger scattering efficiency is due to the diffraction of light at the edges of the particle.

Other observable phenomena, apart from extinction, are also caused by interstellar dust. One of these is the reddening of the light of stars. (This should not be confused with the redshift of spectral lines.) Reddening is due to the fact that the amount of extinction becomes larger for shorter wavelengths. Going from red to ultraviolet, the extinction is roughly inversely proportional to wavelength. For this reason the light of distant stars is redder than would be expected on the basis of their spectral class. The spectral class is defined on the basis of the relative strengths of the spectral lines which are not affected by extinction.

According to (4.20), the observed colour index B — V of a star is

where (B — V )0 is the intrinsic colour of the star and Eb—v the colour excess. As noted in Sect. 4.5 the ratio between the visual extinction Av and the colour excess is approximately constant:

Wavelength À [nm] 1000 500 300 200 125

Wavelength À [nm] 1000 500 300 200 125

R does not depend on the properties of the star or the amount of extinction. This is particularly important in photometric distance determinations because of the fact that the colour excess EB—V can be directly determined from the difference between the observed colour index B — V and the intrinsic colour (B — V )0 known from the spectral class. One can then calculate the extinction

and finally the distance. Since the interstellar medium is far from homogeneous, the colour excess method gives a much more reliable value than using some average value for the extinction in (4.18).

The wavelength dependence of the extinction, A (A.), can be studied by comparing the magnitudes of stars of the same spectral class in different colours. These measurements have shown that A (A) approaches zero as A becomes very large. In practice A(A) can be measured up to a wavelength of about two micrometres. The extrapolation to zero inverse wavelength is then fairly reliable. Figure 15.4a shows A (A) as a function of inverse wavelength. It also illustrates how the quantities A V and EB—V, which are needed in order to calculate the value of R, are obtained from this extinction or reddening curve. Figure 15.4b shows the observed extinction curve. The points in the ultraviolet (A < 0.3 m) are based on rocket measurements.

Fig. 15.4. (a) Schematic representation of the interstellar extinction. As the wavelength increases, the extinction approaches zero. (Drawing based on Greenberg, J. M. (1968): "Interstellar Grains", in Nebulae and Interstellar Matter, ed. by Middle-hurst, B.M., Aller, L.H., Stars and Stellar Systems, Vol. VII (The University of Chicago Press, Chicago) p. 224). (b) Measured extinction curve, normalized to make Eb-v = 1. (Hoyle, F., Narlikar, J. (1980): The Physics-Astronomy Frontier (W. H. Freeman and Company, San Francisco) p. 156. Used by permission)

It is clear from Fig. 15.4b that interstellar extinction is largest at short wavelengths in the ultraviolet and decreases for longer wavelengths. In the infrared it is only about ten percent of the optical extinction and in the radio region it is vanishingly small. Objects that are invisible in the optical region can therefore be studied at infrared and radio wavelengths.

Another observed phenomenon caused by dust is the polarization of the light of the stars. Since spherical particles cannot produce any polarization, the interstellar dust particles have to be nonspherical in shape.

Am

v-^i b

observer

Fig. 15.5. In a homogeneous medium the extinction in magnitudes is proportional to the pathlength traversed. If the extinction in the direction of the galactic pole is Am, then the extinction at the galactic latitude b will be Am/ sin b

15.1 Interstellar Dust

311

If the particles in a cloud are aligned by the interstellar magnetic field, they will polarize the radiation passing through the cloud. The degree of polarization and its wavelength dependence give information on the properties of the dust particles. By studying the direction of polarization in various directions, one can map the structure of the galactic magnetic field.

In the Milky Way interstellar dust is essentially confined to a very thin, about 100 pc, layer in the galactic plane. The dust in other spiral galaxies has a similar distribution and is directly visible as a dark band in the disc of the galaxy (Fig. 18.12b). The Sun is located near the central plane of the galactic dust layer, and thus the extinction in the direction of the galactic plane is very large, whereas the total extinction towards the galactic

Fig. 15.6. The Coalsack is a dark nebula next to the Southern Cross. (Photograph K. Mattila, Helsinki University)

poles may be less than 0.1 magnitudes. This is apparent in the distribution of galaxies in the sky: at high galactic latitudes, there are many galaxies, while near the galactic plane, there is a 20° zone where hardly any galaxies are seen. This empty region is called the zone of avoidance.

If a homogeneous dust layer gives rise to a total extinction of Am magnitudes in the vertical direction, then according to Fig. 15.5, the total extinction at galactic latitude b will be

If the galaxies are uniformly distributed in space, then in the absence of extinction, the number of galaxies per square degree brighter than the magnitude m would be lg N0(m) = 0.6m + C ,

where C is a constant (see Exercise 17.1). However, due to extinction, a galaxy that would otherwise have the apparent magnitude m0 will have the magnitude m(b) = m0 + Am(b) = m0 + Am/ sinb , (15.15)

where b is the galactic latitude. Thus the observable number of galaxies at latitude b will be lg N(m, b) = lg N0(m - Am(b))

Am sin b

Dark Nebulae. Observations of other galaxies show that the dust is concentrated in the spiral arms, in particular at their inner edge. In addition dust is concentrated in individual clouds, which appear as star-poor regions or dark nebulae against the background of the Milky Way. Examples of dark nebulae are the Coalsack in the southern sky (Fig. 15.6) and the Horsehead nebula in Orion. Sometimes the dark nebulae form extended winding bands, and sometimes small, almost spherical, objects. Objects of the latter type are most easy to see against a bright background, e. g. a gas nebula (see Fig. 15.19). These objects have been named globules by Bart J. Bok, who put forward the hypothesis that they are clouds that are just beginning to contract into stars.

The extinction by a dark nebula can be illustrated and studied by means of a Wolf diagram, shown schematically in Fig. 15.7. The diagram is constructed on the basis of star counts. The number of stars per square degree in some magnitude interval (e. g. between magnitudes 14 and 15) in the cloud is counted and compared with the number outside the nebula. In the comparison area, the number of stars increases monotonically towards fainter magnitudes. In the dark nebula the num-

where C = lg N0(m) does not depend on the galactic latitude. By making galaxy counts at various latitudes b, the extinction Am can be determined. The value obtained from galaxy counts made at Lick Observatory is Am pg = 0.51 mag.

The total vertical extinction of the Milky Way has also been determined from the colour excesses of stars. These investigations have yielded much smaller extinction values, about 0.1 mag. In the direction of the north pole, extinction is only 0.03 mag. The disagreement between the two extinction values is probably largely due to the fact that the dust layer is not really homogeneous. If the Sun is located in a local region of low dust content, the view towards the galactic poles might be almost unobstructed by dust.

1000

0.01

1000

0.01

_

-

/ y^

/ Am

1 , ,

Magnitude m

5 10 15

Magnitude m

Fig. 15.7. Wolf diagram. The horizontal coordinate is the magnitude and the vertical coordinate is the number of stars per square degree in the sky brighter than that magnitude. A dark nebula diminishes the brightness of stars lying behind it by the amount Am bers first increase in the same way, but beyond some limiting magnitude (10 in the figure) the number of stars falls below that outside the cloud. The reason for this is that the fainter stars are predominantly behind the

nebula, and their brightness is reduced by some constant amount Am (2 magnitudes in the figure). The brighter stars are mostly in front of the nebula and suffer no extinction.

Antoc-esj

It Sco

JGC 6144

Fig. 15.8a-c. Bright and dark nebulae in Scorpius and Ophiuchus. Photograph (a) was taken in the blue colour region, X = 350-500 nm, and (b) in the red colour region, X = 600-680 nm. (The sharp rings in (b) are reflections of Antares in the correction lens of the Schmidt camera.) The nebulae located in the area are identified in drawing (c). B44 and H4 are dark nebulae. There is a large reflection nebula around Antares, which is faintly visible in the blue (a), but bright in the red (b) regions. Antares is very red (spectral class M1) and therefore the reflec tion nebula is also red. In contrast, the reflection nebulae around the blue stars p Ophiuchi (B2), CD-24° 12684 (B3), 22Scorpii (B2) and a Scorpii (B1) are blue and are visible only in (a). In (b) there is an elongated nebula to the right of a Scorpii, which is invisible in (a). This is an emission nebula, which is very bright in the red hydrogen Ha line (656 nm). In this way reflection and emission nebulae can be distinguished by means of pictures taken in different wavelength regions. (Photograph (a) E. Barnard, and (b) K. Mattila)

Fig. 15.9. The reflection nebula NGC 2068 (M78) in Orion. In the middle of the nebula there are two stars of about magnitude 11. The northern one (at the top) is the illuminating star, while the other one probably lies in the foreground. (Photography Lunar and Planetary Laboratory, Catalina Observatory)

Fig. 15.9. The reflection nebula NGC 2068 (M78) in Orion. In the middle of the nebula there are two stars of about magnitude 11. The northern one (at the top) is the illuminating star, while the other one probably lies in the foreground. (Photography Lunar and Planetary Laboratory, Catalina Observatory)

Reflection Nebulae. If a dust cloud is near a bright star, it will scatter, i. e. reflect the light of the star. Thus individual dust clouds can sometimes be observed as bright reflection nebulae. Some 500 reflection nebulae are known.

The regions in the sky richest in reflection nebulae are the areas around the Pleiades and around the giant star Antares. Antares itself is surrounded by a large red reflection nebula. This region is shown in Fig. 15.8. Figure 15.9 shows the reflection nebula NGC 2068, which is located near a large, thick dust cloud a few degrees northwest of Orion's belt. It is one of the brightest reflection nebulae and the only one included in the Messier catalogue (M78). In the middle of the nebula there are two stars of about 11 magnitudes. The northern star illuminates the nebula, while the other one is probably in front of the nebula. Figure 15.10 shows the reflection nebula NGC 1435 around Merope in the Pleiades. Another bright and much-studied reflection nebula is NGC 7023 in Cepheus. It, too, is connected with a dark nebula. The illuminating star has emission lines in its spectrum (spectral type Be). Infrared stars have also been discovered in the area of the nebula, probably a region of star formation.

In 1922 Edwin Hubble published a fundamental investigation of bright nebulae in the Milky Way. On the basis of extensive photographic and spectroscopic observations, he was able to establish two interesting relationships. First he found that emission nebulae only occur near stars with spectral class earlier than B0, whereas reflection nebulae may be found near stars of spectral class B1 and later. Secondly Hubble discovered a relationship between the angular size R of the nebula and the apparent magnitude m of the illuminating star:

Thus the angular diameter of a reflection nebula is larger for a brighter illuminating star. Since the measured size of a nebula generally increases for longer exposures, i. e. fainter limiting surface brightness, the value of R should be defined to correspond to a fixed limiting surface brightness. The value of the constant in the Hubble relation depends on this limiting surface

Fig. 15.10. The reflection nebula NGC 1435 around Merope (23 Tau, spectral class B6) in the Pleiades. This figure should be compared with Fig. 16.1, where Merope is visible as the lowest of the bright stars in the Pleiades. (National Optical Astronomy Observatories, Kitt Peak National Observatory)

Fig. 15.10. The reflection nebula NGC 1435 around Merope (23 Tau, spectral class B6) in the Pleiades. This figure should be compared with Fig. 16.1, where Merope is visible as the lowest of the bright stars in the Pleiades. (National Optical Astronomy Observatories, Kitt Peak National Observatory)

Fig. 15.11. The Hubble relation for reflection nebulae. The horizontal axis shows the radius R of the nebulae in arc minutes and the vertical axis, the (blue) apparent magnitude m of the central star. No measurements were made in the hatched region. (van den Bergh, S. (1966): Astron. J. 71, 990)

brightness. The Hubble relation for reflection nebulae is shown in Fig. 15.11, based on measurements by Sidney van den Bergh from Palomar Sky Atlas plates. Each point corresponds to a reflection nebula and the straight line represents the relation (15.17), where the value of the constant is 12.0 (R is given in arc minutes).

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